{
  "id": "cond-mat/9705075",
  "version": "v3",
  "published": "1997-05-08T17:22:03.000Z",
  "updated": "1997-05-28T18:32:40.000Z",
  "title": "Scaling and correlation in financial data",
  "authors": [
    "Rama Cont"
  ],
  "comment": "LATEX file + 8 postscript figures.",
  "categories": [
    "cond-mat.stat-mech",
    "adap-org",
    "cond-mat.dis-nn",
    "nlin.AO",
    "physics.data-an",
    "q-fin.ST"
  ],
  "abstract": "The statistical properties of the increments x(t+T) - x(t) of a financial time series depend on the time resolution T on which the increments are considered. A non-parametric approach is used to study the scale dependence of the empirical distribution of the price increments x(t+T) - x(t) of S&P Index futures, for time scales T, ranging from a few minutes to a few days using high-frequency price data. We show that while the variance increases linearly with the timescale, the kurtosis exhibits anomalous scaling properties, indicating a departure from the iid hypothesis. Study of the dependence structure of the increments shows that although the autocorrelation function decays rapidly to zero in a few minutes, the correlation of their squares exhibits a slow power law decay with exponent 0.37, indicating persistence in the scale of fluctuations. We establish a link between the scaling behavior and the dependence structure of the increments : in particular, the anomalous scaling of kurtosis may be explained by \"long memory\" properties of the square of the increments.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1997-05-28T18:32:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "financial data",
      "increments",
      "slow power law decay",
      "financial time series depend",
      "dependence structure"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997cond.mat..5075C"
    }
  }
}